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But when installed correctly it doesn't move.

Yes it does. Wheel turns left, the faring turns left, etc.

The definition of a static aerodynamic device is one that is rigidly attached to the chassis. The brake faring is not attached to the chassis and moves with the movements of the wheels, theoretically being a movable areo device. But like I already said Ferrari were somehow able to convince the FIA is wasn't and now mostly everybody is doing it.